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Engineering Mathematics help

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yasir_ali

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Hey Guys,
I have some questions regarding Math use in Electronics, which some one asked me and i was somewhat unable to answer them. but i want to know the answers of the Questions. the Questions are:

1- How first order and second order defferential equations are helpful in the process of analysis of Electrical Networks?

2-What is the role of initial Condition of Electrical circuits in defferential equations?

3- In what situation Laplace Transform is required?

Thanks
 
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1 - helpful in determining voltage, current and phase of circuits containing inductances and capacitances.

2 - circuits of order 2 or higher are said to be dynamic, that means that the resultant voltage, current and phase depend on the past values of these quantities as well as present conditions. Initial conditions are needed to correctly determine these quanties due to their dynamic nature.

3 - Laplace transforms is just a method of solving the controlling differential equations. They apply to all 2nd and higher order circuits.
 
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Hey Guys,
I have some questions regarding Math use in Electronics, which some one asked me and i was somewhat unable to answer them. but i want to know the answers of the Questions. the Questions are:

1- How first order and second order defferential equations are helpful in the process of analysis of Electrical Networks?

2-What is the role of initial Condition of Electrical circuits in defferential equations?

3- In what situation Laplace Transform is required?

Thanks

Hi there,

I'd like to add a little here too...

First and second order differential equations in particular are easier to solve than the higher order ones so these are used not only to solve circuits that involve one or two energy storage elements but also to help get a grasp of how higher order circuits work because they are so much simpler.
It's a good idea to study these two first and understand the role of some of the variables clearly before moving on to higher order circuits.

Initial conditions in an electrical circuit can be looked at as the initial values that the energy storage elements have before the analysis begins in time. For example, a capacitor may have zero volts or it could have a hundred volts already stored in it before the analysis starts.
Initial conditions help to solve for unknown constants too...knowing what the initial conditions are often help solve for the unknown constant after integration.
It should be noted however that the initial conditions are not always exactly the initial conditions of the energy storage elements themselves, but many times they are.

Laplace Transforms can be used for any circuit involving resistors, capacitors, and inductors with sources also. The Laplace simply transforms the mathematical expression from the time domain to the frequency domain where many times things are easier to work with, and the Inverse Laplace takes it back into the time domain. Laplace Transforms make things easier sometimes.
Laplace Transforms are not particular suited to multivariate solutions however because often finding the inverse requires factoring the denominator, which can be impossible in multivariate situations in higher order systems.

In addition to those studies, it's also a very good idea to look into numerical methods for solving differential equations as these turn out to be very useful sometimes and very interesting too.
 
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Hey! Can some one link me to any website or name a book that explains and shows an example that how they are being use in the Electrical Networks.


Thanks
 
Hi,


You want examples of how Laplace Transforms are used in electrical networks?
 
Yes. please. i want to know how the are use in the electrical networks? mean how to solve electrical networks using Laplace transform, differential equations.
 
Hi there,

Let me first ask you this then...

Do you already know how to evaluate most common electrical networks that contain only resistors?

I could show you a few short examples i guess, but i did find quite a bit on the web doing a search for "Laplace Transform Examples" and similar.

I'll try to get back here with an example, but i need to know your answer to the above question first.
 
yes sure i can solve the voltage and current divider problems based in resistors.

Hi again,

Oh ok that's great. Did you also have tome complex number theory, ie numbers like 2+3j ?
Im trying to get a little background info on you so i know where to start.
 
yes. i have a bit of knowledge about complex number like real and imaginary number are there. and i have solved them but these days they are not in my use.
 
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@ MrAl
Hey! that was simply great. and very helpful thanks a lot.
can you please do one more favor that name a book that can teach me these differential equations, z-transform, Laplace transform, Fourier series mean all the mathematics that we need in electronics to solve our problems. i've learned these all maths but not included electronics in those maths so don't know the value of these maths. so please help me.

Thanks
 
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Hello again,


You can check out "Engineering Circuit Analysis" by Hayt, possibly any edition but i saw online that edition 6 does have Laplace. That will get you started.
For Z transforms you probably have to pick up a book on Digital Signal Processing.

If you have had differential equations you are 80 percent there already :)
 
Hello,
look at this book i found in google and after have view on its contents i think that it is the one i was looking for. the book name is "Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and systems Engineers By Croft Anthony".
But the problem is that i can't find a downloadable link of this book. and i am simply unable to afford to buy the book. so please Can you find the a downloadable link of this book.? i am feeling bad to ask you this. BUT......
 
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hey! bycon
i cannot buy the book. because 1$ in our country equals 84 Rupees.and 38$ becomes 3192 rupees which i cannot afford. so to say that but that's my truth. :(
 
Hi there,


The Hayt books are pretty good really, but i see that that selection you found has a bit more inside it i think. It also has State Space and RK4 and stuff like that, and also contains some stuff on Z transforms, so maybe that would cover more that you may find interesting. I'll look for a download, but i couldnt find downloads of many books not just that one so i dont know if a download of that book exists. Sometimes they dont have one for the book you want.

Sorry that you can not afford it, the best i could do is offer to show you some more examples, but then again it's hard to cover as much as a whole book. I have taught other people on line already, but it does take some time.
 
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